The court filing from the special master Barbara S Jones in the matter of the search warrants executed in April reveals that parties in the case dropped any claim of legal privilege over “12 audio items that were under consideration by the Special Master”.

It is not known whether Trump is featured on the recordings, which were released to the government last Friday.

The former New York mayor Rudy Giuliani, who has been recruited by Trump as a personal lawyer, confirmed last week to the New York Times the existence of a two-minute conversation which included Trump discussing payments to Karen McDougal, who has claimed she had an affair with Trump in 2006, shortly after the birth of his youngest son.

Cohen’s role is being investigated by the Department of Justice, which is considering whether federal campaign finance laws were breached. In New York state, it is legal to make such a tape recording. On Saturday, Giuliani said the conversation had taken place at Trump Tower in New York City.

The developments come after the FBI raided Cohen’s home, hotel room and offices in April, on a referral from the special counsel, Robert Mueller. Cohen has not been charged with any criminal offence.

In April, Trump tweeted that he did not think Cohen would “flip” and cooperate with authorities who are investigating issues including payments to women –including the porn star Stormy Daniels, who also alleged an affair with Trump, which he denies.

However, in an interview with ABC earlier this month, Cohen said: “My wife, my daughter and my son have my first loyalty and always will,” adding: “I put my family and country first.”

On Saturday morning, Trump tweeted: “The good news is that your favorite president did nothing wrong!”

Trump also questioned the legality of both the raids and the tape, writing: “Inconceivable that the government would break into a lawyer’s office (early in the morning) – almost unheard of. Even more inconceivable that a lawyer would tape a client – totally unheard of & perhaps illegal.”

Sources told CNN that earlier this week a court official in New York had ruled the so-called “McDougal recording” privileged, but that Trump’s legal team had waived that privilege.